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Approche incrémentale des preuves automatiques de terminaison

Abstract : Proving termination of a term rewriting system is often harder when the system is large. A divide and conquer strategy cannot be applied directly, thus making automation of proofs for systems with many rules a very difficult task. In order to provide a significant improvement in proving termination, we focus on two critical points : Automating termination proofs and Computing them incrementally, so as to deal with systems of thousands of rules (common in practice) efficiently. We propose a modular approach of term rewriting systems, making the best of their hierarchical structure. We define rewriting modules and then provide a new method allowing to prove termination incrementally. We obtain new and powerful termination criteria for standard rewriting but also for rewriting modulo associativity and commutativity. Our policy of restraining termination itself (thus relaxing constraints over hierarchies components) together with the generality of the module approach are sufficient to express previous results and methods the premisses of which either include restrictions over unions or make a particular reduction strategy compulsory. We describe our implementation of the modular approach. Proofs are fully automated and performed incrementally. Since convenient orderings are simpler, we observe a dramatic speed up in the finding of the proof.
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Contributor : Xavier Urbain <>
Submitted on : Friday, March 8, 2019 - 1:55:34 PM
Last modification on : Wednesday, October 14, 2020 - 3:41:46 AM
Long-term archiving on: : Monday, June 10, 2019 - 2:31:38 PM


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  • HAL Id : tel-02061902, version 1



Xavier Urbain. Approche incrémentale des preuves automatiques de terminaison. Logique en informatique [cs.LO]. Université Paris 11, 2001. Français. ⟨NNT : 2001PA112227⟩. ⟨tel-02061902⟩



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